Physics 2 - Lecture 11: Nuclear Physics - Pham Tan Thi

Nội dung text: Physics 2 - Lecture 11: Nuclear Physics - Pham Tan Thi

1. Nuclear Physics Pham Tan Thi, Ph.D. Department of Biomedical Engineering Faculty of Applied Sciences Ho Chi Minh University of Technology
2. Nuclides and Isotopes • Electron and nucleon masses (12C nucleus is defined to have u = 12.00) Proton: mp = 1.007276 u Neutron: mn = 1.008665 u Electron: me = 0.000548580 u • The atomic number Z is the number of protons in the nucleus. The neutron number, N, is the number of neutrons in the nucleus. A = Z + N • A nuclide is an atom of a particular structure. Each element has nucleus with a specific number of protons. • Nuclide notation: A ZX A: Number of Nucleons Z: Number of Protons (Electrons) • Example: Carbon 12 C; Neutron 1n; Electron 0e; Proton 1 p 1 0 -1 1
3. Magnetic Moments • Like electrons, nucleons have 1/2-integer spin angular momentum, obeying the same relations as electron spin: S = ~ s(s + 1) • The z-component is itself a quantump number as electron spin: 1 Sz = ~ ±2 • The magnitude of the total angular momentum J of the nucleus is also neatly quantized as: J = ~ j(j + 1) with quantized z-component: Jpz = mj~ (mj = 0; ±1; ±2; ; ±j) • When A is even, j is an integer; but A is odd, j is a half-integer • Associated with the nuclear angular moment is a magnetic moment. In the case of a nucleus, the quantity of magnetic moment is nuclear magneton: eh Magnetic moment for the proton and neutron: µN = 2mp msz =2.7928 µN m =1.9130 µ | | | sz| N
4. Nuclear Binding Energy The mass of the 12C atom, made up of 6 protons and 6 neutrons, defines the mass unit u, i.e. it has a mass of exactly 12 u. The individual masses of the protons and neutrons is 6(1.007276 u) + 6(1.008665 u) = 12.095646 u. The difference, 0.0956 u, when converted to energy E = mc2, is the binding energy EB of the nucleus. It is convenient to use the mass-energy equivalent of c2, which is 931.5 MeV/u, so that 0.0956 u => 89.1 MeV is the binding energy of 12C. It is the energy that must be added to separate the nucleons. The quantity EB/c2 is called the mass defect. E = mc2 =(ZM + Nm A M)c2 B H n Z MH is the mass of a hydrogen atom, E = mcnot2 =( justZM its+ proton,Nm A M )alsoc2 includes B H n Z the electrons of the atom
5. Stable Nuclei and Unstable Nuclei Stable Nuclei: • Z:N ≈ 1:1 when Z is small (light) • Z:N ≈ 1:1.5 when Z is large (heavy) Unstable Nuclei: Most nuclei out of these ranges are unstable
6. Radioactivity • Unstable nuclei decay to more stable nuclei • An isotope can emit 3 types of radiation in the process 4 α particles: 2He nuclei β particles: e− or e+ γ rays: high energy photons A positron (e+) is the antiparticle of the electron (e-)
7. Beta Decay • In a nucleus with too many protons or too many neutrons, beta decay takes place when one of the protons or neutrons is transformed into the other. • The number of nucleons, A, does not change after decaying process; the number of protons is increased or decreased. • There are three types of beta decays: beta-minus, beta-plus and electron capture.
8. Characteristics of Decays
9. Activities and Half-lives • To find the half-life, just determine when No t 1 N = and e = 2 2 ln2 t = t = 1/2 • If you start with No nuclei, after a half-life you will have No/2, and after another half- life you will have No/4, etc. • The quantity 1/λ is called the mean lifetime. An established unit of radioactivity (-dN/dt) is called Curie: 1 Ci = 3.70 x 1010 decay/s In SI units, 1 decay/s is called Becquerel (Bq)
10. Example Activity of 57Co. The isotope 57Co decays by electron capture to 57Fe with a half-life of 272 d. The 57Fe nucleus is produced in an excited state, and it almost instantaneously emits gamma rays that we can detect. (a) Find the mean lifetime and decay constant for 57Co (b) If the activity of 57Co radiation sources is now 2.00 µCi, how many 57Co nuclei do the source contain? (c) What will be the activity after 1 year?
11. Example Radiocarbon dating. The isotope 14C via beta-minus decay to 14N with a half-life of 5730 years. Before 1900, the activity per unit mass of atmospheric carbon due to the presence of 14C averaged about 0.255 Bq per gram of carbon. (a) What fraction of carbon atoms were 14C? (b) In analyzing an archaeological specimen containing 500 mg of carbon, you observe 174 decays in one hour. What is the age of the specimen?
12. Nuclear Fission • Nuclear fission is a decay process in which an unstable nucleus splits into two fragments (the fission fragments) of comparable mass.